Figure 4. Probability distribution functions of particle displacements in the Hele–Shaw experiments.

(a,b) Evolution of the PDF of displacements PDF_Δt(Δx) of the colloids with the time interval Δt when considering the jumps (blue curves) or not (red curves) for N_c=(4.84±0.13) × 10⁶ cells ml⁻¹. The curves have been shifted and separated into two figures for clarity. a corresponds to Δt∈[0.04, 0.8]s, while b corresponds to Δt∈[1.2, 48]s (colour bars: Δt in seconds). Both distributions exhibit exponential-like tails at short time which reflect the presence of loop-like perturbations and jumps in the dynamics. (c,d) Modified kurtosis κ of the PDF of displacements as a function of the time interval Δt with/without jumps respectively. The colours code for the cell concentration (unit: 10⁶ cells ml⁻¹). The PDFs with jumps show slower convergence to the Gaussian limit, as the plots in a,b also suggest.